Problem: Express your answer as a mixed number simplified to lowest terms. $3\dfrac{4}{9}-1\dfrac{9}{15} = {?}$
Answer: Simplify each fraction. $= {3\dfrac{4}{9}} - {1\dfrac{3}{5}}$ Find a common denominator for the fractions: $= {3\dfrac{20}{45}}-{1\dfrac{27}{45}}$ Convert ${3\dfrac{20}{45}}$ to ${2 + \dfrac{45}{45} + \dfrac{20}{45}}$ So the problem becomes: ${2\dfrac{65}{45}}-{1\dfrac{27}{45}}$ Separate the whole numbers from the fractional parts: $= {2} + {\dfrac{65}{45}} - {1} - {\dfrac{27}{45}}$ Bring the whole numbers together and the fractions together: $= {2} - {1} + {\dfrac{65}{45}} - {\dfrac{27}{45}}$ Subtract the whole numbers: $=1 + {\dfrac{65}{45}} - {\dfrac{27}{45}}$ Subtract the fractions: $= 1+\dfrac{38}{45}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{38}{45}$